We propose a method to estimate the probability of earthquake growth to a catastrophic one immediately after observing its initiation, for practical usage in an earthquake early warning system. This method is essentially an application of the conditional probability theory, where the magnitude-frequency relation plays a crucial role. We apply it to the Nankai trough region, Japan, where a catastrophic earthquake is expected in the near future. Based on the historical catalogue, we estimate the probability density of magnitude using a Bayesian approach. We then estimate the probability of earthquake growth to a catastrophic one. If the observed earthquake magnitude reaches 6.5, the estimated probability that the final magnitude exceeds 7.5 is 25--41%. According to previous studies, the time taken for the magnitude to increase from 6.5 to 7.5 is approximately 10--15 seconds. Our method is highly beneficial in that it enables an earlier alarm to be issued.